Convergence Non-Convergence of the XC functional in the sense of a Taylor series

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asked Oct 20, 2021 at 21:36

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Convergence of the XC functional in the sense of a Taylor series

When it comes to improving the accuracy of DFT calculations, there is a well known hierarchy:

starting from LDA using $E_{xc}[n]$,
proceeding with GGA and its $E_{xc}[ n, \nabla n]$ dependency
and finally meta-GGAs with $E_{xc}[ n, \nabla n, \nabla^2n~\text{or}~\nabla^2\phi_i]$

I always wondered why higher order derivatives are not used but never really looked into it. Recently I heard from an expert in the field that it can be shown that $E_{xc}[n]$ can not converge in the sense of a Taylor series.

How? Why?

I just couldn't find more on this matter.

density-functional-theory exchange-correlation

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Convergence Non-Convergence of the XC functional in the sense of a Taylor series

Convergence of the XC functional in the sense of a Taylor series